Īn analysis of ten million games with the default layout, "the turtle", found that about 3 percent of the turtles cannot be solved even when looking below tiles is allowed. In this case, however, it is NP-complete to decide whether all tiles can be removed. The perfect-information version of this puzzle is where the player knows, before the game starts, the position of every tile. It has been proven that it is PSPACE-hard to approximate the maximum probability of removing all tiles within a factor of n ϵ, assuming that there are arbitrarily many quadruples of matching tiles and that the hidden tiles are uniformly distributed. Playing Mahjong solitaire optimally in the sense to maximize the probability of removing all tiles is PSPACE-complete, and the game is NP-complete if looking below tiles is allowed. The game is won when all pairs of tiles have been removed from the board, and lost if the remaining tiles contain no exposed pairs. The goal is to match open pairs of identical tiles and remove them from the board, exposing the tiles under them for play. A tile is said to be open or exposed if it can be moved either left or right without disturbing other tiles.
The 144 tiles are arranged in a four-layer pattern with their faces upwards. An untouched turtle formation, with exposed "free" tiles highlighted in blue
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